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When carbon dioxide is passed through lime water, it turns milky due to the formation of:
A. $CaC{ O }_{ 3 }$
B. $CaO$
C. ${ H }_{ 2 }{ CO }_{ 3 }$
D. $Ca({ HCO }_{ 3 }{ ) }_{ 2 }$

Answer
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Hint: Lime water refers to the solution of calcium hydroxide in water. It is alkaline in nature. The lime water test is widely used in order to determine whether the particular gas is carbon dioxide or not.

Complete step by step answer:
Let us first understand about lime. Lime is made by heating limestone to high temperatures (a process called calcination) in horizontal rotating kilns that are several metres in diameter and are about 100 metres in length. The temperature at which limestone is heated to lime is about 1100-1200°C.
Given below is the method of its preparation:
$\begin{matrix} Ca{ CO }_{ 3 } \\ limestone \end{matrix}\xrightarrow { 1100-120{ 0 }^{ o }C } \begin{matrix} CaO(s) \\ lime \end{matrix}+\begin{matrix} C{ O }_{ 2 }(g) \\ Carbon\quad dioxide \end{matrix} $
When lime (basic in nature) is added to water, it forms slaked lime (calcium hydroxide). Calcium hydroxide is basic in nature, therefore when it is dissolved in water it sparingly dissolves in it since its solubility product is low and forms an alkaline solution called lime water which turns milky when carbon dioxide is passed through it due to the formation of calcium carbonate. This is summarized in the following reactions:
$\begin{matrix} Ca{ O(s) } \\ lime \end{matrix}+\begin{matrix} { H }_{ 2 }O(l) \\ water \end{matrix}\longrightarrow \begin{matrix} Ca(O{ H{ ) }_{ 2 }(s) } \\ slaked\quad lime \end{matrix} $
$\begin{matrix} Ca{ (OH{ ) }_{ 2 }(s) } \\ slaked\quad lime \end{matrix}+\begin{matrix} { H }_{ 2 }O(l) \\ water \end{matrix}\longrightarrow \begin{matrix} Ca(O{ H{ ) }_{ 2 }(aq) } \\ lime\quad water \end{matrix} $
$\begin{matrix} Ca{ (OH{ ) }_{ 2 }(aq) } \\ lime\quad water \end{matrix}+\begin{matrix} { CO }_{ 2 }(g) \\ carbon\quad dioxide \end{matrix}\xrightarrow { the\quad solution\quad turns\quad milky } \begin{matrix} Ca{ CO }_{ 3 }(s) \\ calcium\quad carbonate \end{matrix}$
Hence the correct option is (a) $CaC{ O }_{ 3 }$
Note: Do not get confused between slaked lime and lime water. Slaked lime refers to calcium hydroxide in its solid form while we get lime water when slaked lime is dissolved in water. They are often used to paint the mud houses.